Non-archimedean Sendov's Conjecture

Abstract

We prove non-archimedean analogue of Sendov's conjecure. We also provide complete list of polynomials over an algebraically closed non-archimedean field $K$ that satisfy the optimal bound in the Sendov's conjecture.

4 pages, criterion for polynomials of degree $n$ with $v(n)=0$ is added

Cited by in corpus (2)

• C*-algebraic Gauss-Lucas Theorem and C*-algebraic Sendov's Conjecture
• On geometry of p-adic polynomials